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5. 一块矩形木板采用如图所示的方式在木板上截出两个面积分别为$8\mathrm{cm}^2$和$50\mathrm{cm}^2$的正方形木板后，剩余的木板(阴影部分)的面积为(
A.$42$
B.$27$
C.$12$
D.$10$
C
)$\mathrm{cm}^2$A.$42$
B.$27$
C.$12$
D.$10$
答案
5. C
6. 化简.
(1) $\sqrt{\dfrac{4}{3}}$ =
(2) $\dfrac{3}{4}\sqrt{a^{2n}b^{2n + 1}}(a ＞ 0, b ＞ 0)$ =
(3) $\dfrac{1}{\sqrt{5} - 2}$ =
(4) $(1 - a)\sqrt{\dfrac{-1}{a - 1}}$ =
(1) $\sqrt{\dfrac{4}{3}}$ =
$\dfrac{2}{3}\sqrt{3}$
；(2) $\dfrac{3}{4}\sqrt{a^{2n}b^{2n + 1}}(a ＞ 0, b ＞ 0)$ =
$\dfrac{3a^{n}b^{n}}{4}\sqrt{b}$
；(3) $\dfrac{1}{\sqrt{5} - 2}$ =
$\sqrt{5}+2$
；(4) $(1 - a)\sqrt{\dfrac{-1}{a - 1}}$ =
$\sqrt{1 - a}$
.答案
6. (1) $\dfrac{2}{3}\sqrt{3}$ (2) $\dfrac{3a^{n}b^{n}}{4}\sqrt{b}$ (3) $\sqrt{5}+2$ (4) $\sqrt{1 - a}$
7. 计算.
(1) $2\sqrt{\dfrac{3}{4}} × \dfrac{3}{2}\sqrt{21}$；
(2) $\dfrac{\sqrt{12} + \sqrt{27}}{\sqrt{3}}$；
(3) $(3 + \sqrt{2})^2$；
(4) $(5\sqrt{48} - 6\sqrt{27} + \sqrt{12}) ÷ \sqrt{3}$；
(5) $(1 - 2\sqrt{3})(1 + 2\sqrt{3}) + (1 + 2\sqrt{3})^2$.
(1) $2\sqrt{\dfrac{3}{4}} × \dfrac{3}{2}\sqrt{21}$；
(2) $\dfrac{\sqrt{12} + \sqrt{27}}{\sqrt{3}}$；
(3) $(3 + \sqrt{2})^2$；
(4) $(5\sqrt{48} - 6\sqrt{27} + \sqrt{12}) ÷ \sqrt{3}$；
(5) $(1 - 2\sqrt{3})(1 + 2\sqrt{3}) + (1 + 2\sqrt{3})^2$.
答案
7. (1) $\dfrac{9}{2}\sqrt{7}$ (2) 5 (3) $11+6\sqrt{2}$ (4) 4 (5) $2+4\sqrt{3}$
